It is hoped the promise of extra cash will achieve the EU’s demand for “sufficient progress” on divorce issues and allow EU leaders to sanction the start of the second phase of exit talks at a key summit next month.

But, on Tuesday, the Irish Government repeated its warning that settling the Brexit bill is not the only barrier to progression.

In an interview with the Evening Standard, Irish foreign minister Simon Coveney said: “Anybody who thinks that just because the financial settlement issue gets resolved… that somehow Ireland will have a hand put on the shoulder and be told, ‘Look, it’s time to move on.’

Yet, senior Government figures on Tuesday put pressure back on Brussels and the remaining 27 EU member states over the issue.

The Prime Minister, speaking from Downing Street after meeting Northern Irish politicians, said: “We recognise the issue of the border between Northern Ireland and the Republic of Ireland.

“We want to see people continuing to move across that border, to trade across that border.

“It’s important for the economies of Northern Ireland and the Republic of Ireland, but it’s also important for people in their day-to-day lives.

Mrs May added: “We want to move on to having those more detailed discussions about what that trade relationship will be for the future.

“The EU has made clear that’s an issue for phase two, we want to be able to move on to do that.”

Meanwhile, Foreign Secretary Mr Johnson said “there’s no question the issue of the border is very live in Irish politics” and repeated the Government’s commitment to seeking a solution.

Answering questions in the House of Commons, the Vote Leave figurehead said: “There can be no hard border, that would be unthinkable.

“It would be economic and political madness and we certainly, I think everybody on both sides of this House, understands the social, political and spiritual ramifications of allowing any such thing to happen.

“That’s why it’s so important that we get on to the second phase of the negotiations, that we get sufficient progress at the European Council in December and we’re able to debate these issues in proper.”

Labour’s Emily Thornberry urged Mr Johnson to make the possible establishment of a hard border a resigning issue for him.

Delivering a speech to a summit in Westminster, Mr Davis became the third Government minister to put pressure on the EU to advance Brexit talks.

The Brexit Secretary said: “It’s becoming clearer with each new negotiating round we must start talking about our future relationship.

“The Northern Ireland border cannot be fully addressed if we’re not taking into account the shape of our future partnership with the EU.”

Mr Davis insisted the UK is “ready to begin that conversation as soon as the EU are”.